Conventionally, various methods have been proposed as image-processing methods which apply conversion processes to an input image with n(n-1) gray scales so as to convert the resolution and magnification of the image and obtain an output image with n gray scales.
With respect to methods for converting the resolution of an image, a simple interpolation method, which uses pixel values prior to an interpolation as peripheral interpolated pixel values after the interpolation has been carried out as shown in FIG. 7(a), and an average method, which uses the average value of pixel values prior to an interpolation as pixel values after the interpolation has been carried as shown in FIG. 7(b), have been known.
Moreover, a linear interpolation method, which connects respective pixel values with straight lines prior to an interpolation and which uses values on the straight lines as interpolation values, for example, as shown in FIG. 7(c), is known as another method for converting the resolution of an image. At present, this linear interpolation method is most widely adopted.
With respect to methods for converting the magnification of an image, a simple interpolation method, which uses pixel values prior to an interpolation as peripheral varied magnification pixel values after the interpolation has been carried out as shown in FIG. 8(a), and an average method, which uses the average value of pixel values prior to an interpolation as varied magnification pixel values after the interpolation has been carried out as shown in FIG. 8(b), have been known.
Moreover, a linear interpolation method, which connects respective pixel values with straight lines prior to an interpolation and which uses values on the straight lines as interpolation values, for example, as shown in FIG. 8(c), is known as another method for converting the resolution of an image. At present, this linear interpolation method is most widely adopted.
The above-mentioned methods, however, cause a problem in which an image, which has been subjected to the resolution-converting process or the variable-magnification process, has blurred edge portions or burred slanting lines, resulting in a lack of smoothness.
In order to solve this problem, for example, "Image-Interpolating Apparatus", disclosed in Japanese Laid-Open Patent Publication 12486/1994 (Tokukaihei 6-12486), carries out a non-linear enlarging process on an input image by using a neural network so that the image that appears after the process has sharpness in its edge portions and has its burred slanting lines masked, resulting in a smooth image.
The enlarging process in the image-interpolating apparatus in the above-mentioned laid-open patent publication is explained as follows: First, four pixel regions including a focused pixel, its right-hand adjacent pixel, its lower adjacent pixel and its diagonal lower adjacent pixel are extracted from a binary image. Next, provided that the values of the pixels in the four pixel regions are altered, that is, provided that the focused pixel is enlarged K times in the main scanning direction and L times in the sub-scanning direction, pixels in the enlarged region are statistically analyzed to find such pixels in the enlarged region as to be smoothly connected to the peripheral pixels, and by using the results as teaching signals and the values of the respective pixels in the four pixel regions as input signals, a learning operation for the neural network is preliminarily carried out. Then, the enlarging process of the inputted binary image is carried out by using the neural network after having been subjected to the learning operation.
However, in the enlarging process by the image-interpolating apparatus as disclosed in the above-mentioned laid-out patent publication, since the neural network, which has been subjected to a learning operation using statistical data that has been preliminarily provided, is adopted, weights at the connecting sections of the neural network after the learning operation has been carried out are fixed. For this reason, fine adjustments of the weights cannot be made by applying re-learning operations; thus, the resulting problem is that in the case of insufficient statistical data, it is not possible to obtain smoothly enlarged images depending on various input images.